The monthly sales of mufflers in the Richmond Virginia area

The monthly sales of mufflers in the Richmond, Virginia, area follow the normal distribution with a mean of 1,200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5 percent chance of running out of stock. Where should the manufacturer set the inventory levels? Denote X to be the random variable \"monthly sales of mufflers\", and x to be the right inventory level the manufacturer sets, choose from the followings the correct way to set up for x:

Solution

mu = 1200

sigma = 225

Let inventory level be x

X - monthly sales

Hence the prob for sales below inventory should be 0.95

P(X<=x) = 0.95 is the correct answer.